A133866 Decimal expansion of the smallest positive fixed point of csc(x) (and csc^-1(x)).

1, 1, 1, 4, 1, 5, 7, 1, 4, 0, 8, 7, 1, 9, 3, 0, 0, 8, 7, 3, 0, 0, 5, 2, 5, 1, 7, 8, 1, 6, 9, 2, 0, 3, 9, 0, 3, 9, 5, 4, 1, 0, 1, 3, 7, 6, 0, 4, 9, 3, 7, 5, 5, 9, 5, 3, 3, 7, 3, 7, 0, 5, 5, 5, 3, 5, 1, 0, 1, 9, 1, 3, 5, 4, 5, 0, 0, 8, 8, 8, 2, 6, 3, 4, 0, 4, 6, 4, 5, 4, 2, 8, 1, 7, 4, 6, 8, 9, 4, 9, 2, 9, 8, 6, 7

Offset: 1

Author

Eric W. Weisstein, Sep 27 2007

Keywords

• nonn
• cons

Examples

			1.1141571408719300873...
		

References

• Mohammad K. Azarian, On the Fixed Points of a Function and the Fixed Points of its Composite Functions, International Journal of Pure and Applied Mathematics, Vol. 46, No. 1, 2008, pp. 37-44. Mathematical Reviews, MR2433713 (2009c:65129), March 2009. Zentralblatt MATH, Zbl 1160.65015.
• Mohammad K. Azarian, Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60. Solution published in Vol. 39, No. 1, January 2008, pp. 66-67.

Links

• Eric Weisstein's World of Mathematics, Cosecant
• Eric Weisstein's World of Mathematics, Fixed Point
• Index entries for transcendental numbers.

Programs

Mathematica

x /. FindRoot[Csc[x] == x, {x, 1}, WorkingPrecision -> 105] // RealDigits // First (* Jean-François Alcover, Feb 06 2013 *)

PARI

solve(x=1,2, x*sin(x)-1) \\ Charles R Greathouse IV, Feb 03 2025